For instance the RV can be the sum of squared daily returns for a particular month, which would yield a measure of price variation over this month.
More commonly, the realized variance is computed as the sum of squared intraday returns for a particular day.
The realized volatility is the square root of the realized variance, or the square root of the RV multiplied by a suitable constant to bring the measure of volatility to an annualized scale.
For instance, if the RV is computed as the sum of squared daily returns for some month, then an annualized realized volatility is given by
Under ideal circumstances the RV consistently estimates the quadratic variation of the price process that the returns are computed from.
[2] Ole E. Barndorff-Nielsen and Neil Shephard (2002), Journal of the Royal Statistical Society, Series B, 63, 2002, 253–280.
is some (possibly random) process for which the integrated variance, is well defined.
the realized variance converges to IV in probability.
When prices are measured with noise the RV may not estimate the desired quantity.
[3] This problem motivated the development of a wide range of robust realized measures of volatility, such as the realized kernel estimator.